How to find integer nth roots?

Question

I want to find the greatest integer less than or equal to the kth root of n. I tried

int(n**(1/k))

But for n=125, k=3 this gives the wrong

Answer 1

I wonder if starting off with a method based on logarithms can help pin down the sources of rounding error. For example:

import math
def power_floor(n, k):
    return int(math.exp(1.0 / k * math.log(n)))

def nth_root(val, n):
    ret = int(val**(1./n))
    return ret + 1 if (ret + 1) ** n == val else ret

cases = [
    (124, 3),
    (125, 3),
    (126, 3),
    (1, 100),
    ]


for n, k in cases:
    print "{0:d} vs {1:d}".format(nth_root(n, k), power_floor(n, k))

prints out

4 vs 4
5 vs 5
5 vs 5
1 vs 1